Answer:
The equation of the line segment AB is:
[tex]y = -2x+11[/tex]
The graph of the line segment AB is also attached.
Step-by-step explanation:
Given the points
Determining the slope between A(3,5) and B(5,1)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(3,\:5\right),\:\left(x_2,\:y_2\right)=\left(5,\:1\right)[/tex]
[tex]m=\frac{1-5}{5-3}[/tex]
[tex]m=-2[/tex]
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = -2 and the point (3, 5) in the equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y - 5 = -2(x-3)[/tex]
[tex]y-5 = -2x+6[/tex]
[tex]y = -2x+6+5[/tex]
[tex]y = -2x+11[/tex]
Therefore, the equation of the line segment AB is:
[tex]y = -2x+11[/tex]
The graph of the line segment AB is also attached.
